A Bayesian Approach For The Consideration Of Measurement Errors

Abstract

Metrology is a key tool for tolerancing as it is used to determine whether dimensions are within their tolerance intervals. However, measurement errors cannot be avoided and need being accounted for. The probabilistic approach is applied to both the dimensions and their measurement errors; they are modelled as random variables and characterized by their probability density function. The probability density function of the measurement error is assumed to be known; this work is included in a research project in collaboration with a metrology company, where the engineers are able to provide us with this information. This paper describes a strategy to account for such measurement errors and (partially) correct or mitigate their effects. Through Bayesian inference, the likelihood of true values given measured values is estimated, allowing for a probabilistic correction. The proposed method is applied to numerical examples with simulated data and its relevance is discussed.